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Toric periods and p-adic families of modular forms of half-integral weight
The primary goal of this work is to construct p-adic families of modular forms of half-integral weight, by using Waldspurger's automorphic framework to make the results as comprehensive and precise as possible. A secondary goal is to clarify the role of test vectors as defined by Gross-Prasad i...
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| Auteur principal : | |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Toric periods and p-adic families of modular forms of half-integral weight / V. Vatsal |
| Publié : |
Providence (R.I.) :
American Mathematical Society
, 2023 |
| Description matérielle : | 1 volume (V-95 p.) |
| Collection : | Memoirs of the American Mathematical Society ; 1438 |
| Sujets : | |
| Documents associés : | Autre format:
Toric periods and p-adic families of modular forms of half-integral weight |
| Résumé : | The primary goal of this work is to construct p-adic families of modular forms of half-integral weight, by using Waldspurger's automorphic framework to make the results as comprehensive and precise as possible. A secondary goal is to clarify the role of test vectors as defined by Gross-Prasad in the elucidation of general formulae for the Fourier coefficients of modular forms of half-integral weight in terms of toric periods of the corresponding modular forms of integral weight. As a consequence of our work, we develop a generalization of a classical formula due to Shintani, and make precise the conditions under which Shintani's lift vanishes. We also give a number of results to test vectors for ramified representations which are of independent interest |
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| Bibliographie : | Bibliographie p.93-95 |
| ISBN : | 978-1-4704-6550-6 |